Sample surveys oftentimes provide weights to convert sample estimates into
representative population figures. Sometimes such frequency weights are not
integers (For example, National Health and Nutrition Examination Survey
III). It seems that Stata can only deal with integer frequency weights. Is
there a solution? The best that I can do right now is to take the nearest
integer to the non-integer frequencies. This method seems rather adhoc. Any
help will be deeply appreciated.

I think iweights will work, at least if the command allows the use of
iweights. e.g. I just tried